Time Series Analysis in Climatology and Related Sciences

Acknowledgements
Contents
Abbreviations
1 Introduction
References
2 Basics of Scalar Random Processes
2.1 Basic Statistical Characteristics
2.2 Deterministic Process
2.3 Random Process
2.4 Covariance and Correlation Functions
2.5 Spectral Density
2.6 Examples of Geophysical Time Series and Their Statistics
References
3 Time and Frequency Domain Models of Scalar Time Series
3.1 Nonparametric Spectral Analysis
3.2 Parametric Models of Time Series
3.3 Parametric Spectral Analysis
3.4 Determining the Order of Autoregressive Models
3.5 Comparison of Autoregressive and Nonparametric Spectral Estimates
3.6 Advantages and Disadvantages of Autoregressive Analysis (Scalar Case)
References
4 Practical Analysis of Time Series
4.1 Selecting the Sampling Interval
4.2 Linear Trend and Its Analysis
4.3 Testing for Stationarity and Ergodicity
4.4 Linear Filtering
4.5 Frequency Resolution of Autoregressive Spectral Analysis
4.6 Example of AR Analysis in Time and Frequency Domains
Appendix
References
5 Stochastic Models and Spectra of Climatic and Related Time Series
5.1 Properties of Climate Indices
5.2 Properties of Time Series of Spatially Averaged Surface Temperature
5.3 Quasi-Biennial Oscillation
5.4 Other Oscillations
Appendix
References
6 Statistical Forecasting of Geophysical Processes
6.1 General Remarks
6.2 Method of Extrapolation
6.3 Example 1. Global Annual Temperature
6.4 Example 2. Quasi-Biennial Oscillation
6.5 Example 3. ENSO Components
6.6 Example 4. Madden–Julian Oscillation
Appendix
References
7 Bivariate Time Series Analysis
7.1 Elements of Bivariate Time Series Analysis
7.1.1 Bivariate Autoregressive Models in Time Domain
7.1.2 Bivariate Autoregressive Models in Frequency Domain
7.1.3 Reliability of Autoregressive Estimates of Frequency-Dependent Quantities
7.2 Granger Causality and Feedback
7.3 On Properties of Software for Analysis of Multivariate Time Series
References
8 Teleconnection Research and Bivariate Extrapolation
8.1 Example 1. The ENSO Teleconnection
8.2 Example 2. Teleconnections Between ENSO and AST
8.2.1 Time Domain Analysis—ENSO and Spatially Averaged Temperature
8.2.2 Frequency Domain Analysis
8.3 Example 3. Bivariate Extrapolation of Madden–Julian Oscillation
Appendix
References
9 Reconstruction of Time Series
9.1 Introduction
9.2 Methods of Reconstruction
9.2.1 Traditional Correlation/Regression Reconstruction (CRR)
9.2.2 Autoregressive Reconstruction Method (ARR)
9.3 Verification of the Autoregressive Reconstruction Method
9.3.1 Reconstruction Example: A Climatic Type Process
9.4 Discussion and Conclusions
References
10 Frequency Domain Structure and Feedbacks in QBO Time Series
References
11 Verification of General Circulation Models
11.1 Verifying the Structure of ENSO
11.1.1 Linear Trend Rates
11.1.2 Mean Values and Standard Deviations
11.1.3 Probability Density
11.1.4 Time and Frequency Domain Properties
11.2 Verification of ENSO Influence upon Global Temperature
11.3 Verifications of Properties of Surface Temperature Over CONUS
11.4 Conclusions
References
12 Applications to Proxy Data
12.1 Introduction
12.2 Greenland Ice Cores
12.3 Antarctic Ice Cores
12.4 Discussion and Conclusions
References
13 Application to Sunspot Numbers and Total Solar Irradiance
13.1 Introduction
13.2 Properties of Sunspot Number Time Series
13.3 Properties of Total Solar Irradiance Time Series
References
14 Multivariate Time and Frequency Domain Analysis
14.1 Time Domain Analysis
14.2 Frequency Domain Analysis
14.3 Analysis of a Simulated Trivariate Time Series
14.3.1 Time Domain Analysis
14.3.2 Frequency Domain Analysis
14.4 Analysis of Climatic Time Series
References
15 Summary and Recommendations
References